[1]}, [2]}, and [3]}
propose extensions to the prior in (REF ) for simultaneous variable
selection and clustering. They use a mixture of a point mass at zero with a
Dirichlet process prior   G = 0 0 +
(1 - 0) G*,  G* DP(G0, )  where \(0 \le \pi _0 \le 1\)  is a mixture weight, \(\delta _0\)  is a point mass probability density at 0,
and \(DP(G_0, \alpha )\)  is a Dirichlet Process prior with precision \(\alpha \)  and
base measure \(G_0\) . Using the constructive definition of
[4]} the prior in (REF ) is again an
infinite mixture of point masses with the first point mass fixed at zero
 
G = 0 0 + (1 - 0) k = 1 k
k = k = 0 k k

where \(\tilde{\pi }_0 = \pi _0\) , \(\tilde{\pi }_k = (1 - \pi _0) \pi _k\)  if \(k \ge 1\) , \(\theta _0 = 0\)  and \(\theta _k \overset{iid}{\sim }G_0\)  if \(k \ge 1\) . Computation for
this model is similar to the model discussed in (REF ) because the
prior in (REF ) can be interpreted as a clustering prior with
the restriction that the first cluster is zero. We can account for this
restriction by making a few changes to the Gibbs sampler developed by
[5]}.
